Turbine Nozzle Airfoil Profile

ABSTRACT

The present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

FIELD

The present application relates generally to a turbine nozzle for a gasturbine engine, and more particularly relates to a turbine nozzleairfoil profile for a turbine nozzle.

BACKGROUND

Some aircraft and/or power plant systems, for example certain jetaircraft, nuclear, simple cycle and combined cycle power plant systems,employ turbines (also referred to as turbomachines) in their design andoperation. Some of these turbines employ airfoils (e.g., stator vanes ornozzles and rotor blades.) which during operation are exposed to fluidflows. These airfoils are configured to aerodynamically interact withthe fluid flows and generate energy (e.g., creating thrust, turningkinetic energy to mechanical energy, thermal energy to mechanicalenergy, etc.) from these fluid flows as part of power generation. As aresult of this interaction and conversion, the aerodynamiccharacteristics and losses of these airfoils have an impact on systemand turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages are set forth below in the following description,or may be obvious from the description, or may be learned throughpractice.

The present application provides a turbine nozzle including an airfoilshape. The airfoil shape may have a nominal profile substantially inaccordance with Cartesian coordinate values of X, Y and Z set forth inTable I. The Cartesian coordinate values of X, Y and Z arenon-dimensional values from 0% to 100% convertible to dimensionaldistances in inches by multiplying the Cartesian coordinate values of X,Y and Z by a height of the airfoil in inches. The X and Y values, whenconnected by smooth continuing arcs, define airfoil profile sections ateach distance Z. The airfoil profile sections at Z distances beingjoined smoothly with one another to form a complete airfoil shape.

The present application further provides a turbine nozzle including anairfoil having a suction-side uncoated nominal airfoil profilesubstantially in accordance with suction-side Cartesian coordinatevalues of X, Y and Z set forth in Table I. The Cartesian coordinatevalues of X, Y and Z are non-dimensional values from 0% to 100%convertible to dimensional distances in inches by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil ininches. The X and Y values, when connected by smooth continuing arcs,define airfoil profile sections at each Z distance. The airfoil profilesections at the Z distances may be joined smoothly with one another toform a complete suction-side airfoil shape. The X, Y and Z distancesbeing scalable as a function of the same constant or number to provide ascaled-up or scaled-down airfoil.

The present application further provides a turbine with a number ofturbine nozzles having an airfoil having an airfoil shape. The airfoilshaving a nominal profile substantially in accordance with Cartesiancoordinate values of X, Y and Z set forth in Table I. The Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances in inches by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil ininches. The X and Y values, when connected by smooth continuing arcs,define airfoil profile sections at each Z distance. The airfoil profilesections at the Z distances may be joined smoothly with one another toform a complete airfoil shape.

Those of ordinary skill in the art will better appreciate the featuresand aspects of such embodiments, and others, upon review of thespecification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including thebest mode thereof to one skilled in the art, is set forth moreparticularly in the remainder of the specification, including referenceto the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine havingmultiple stages with each stage including alternating rows of turbinerotor blades and turbine nozzles according to at least one embodiment ofthe present disclosure;

FIG. 2 is a perspective view of an exemplary turbine nozzle according toat least one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of theturbine nozzle of FIG. 2.

DETAILED DESCRIPTION

Referring now to the drawings, particularly to FIG. 1, there isillustrated an exemplary turbine 10 of a gas turbine 12 including aplurality of turbine stages arranged in serial flow order. Each stage ofthe turbine includes a row of turbine nozzles or vanes disposed axiallyadjacent to a corresponding row of turbine rotor blades. Four stages areillustrated in FIG. 1. The exact number of stages of the turbine 10 is achoice of engineering design, and may be more or less than the fourstages illustrated in FIG. 1. The four stages are merely exemplary ofone turbine design, and are not intended to limit the presently claimedturbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100and a plurality of turbine rotor blades 150. The turbine nozzles 100 areannularly arranged about an axis of a turbine rotor 14. The turbinerotor blades 150 are annularly arranged about and coupled to the turbinerotor 14. A second stage of the turbine 12 includes a plurality ofturbine nozzles 200 annularly arranged about the axis of the turbinerotor 14 and a plurality of turbine rotor blades 250 annularly arrangedabout and coupled to the turbine rotor 14. The turbine nozzles 200 maybe coupled to a casing 16 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a pluralityof turbine nozzles 300 annularly arranged about the axis of the turbinerotor 14 and a plurality of turbine rotor blades 350 annularly arrangedabout and coupled to the turbine rotor 14. The turbine nozzles 300 maybe coupled to the casing 16 of the turbine 12. In particularembodiments, the turbine 12 includes a fourth stage which includesplurality of turbine nozzles 400 annularly arranged about the axis ofthe turbine rotor 14 and a plurality of turbine rotor blades 450annularly arranged about and coupled to the turbine rotor 14. The fourthstage turbine nozzles 400 may be coupled to the casing 16 of the turbine12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400and turbine rotor blades 150, 250, 350 and 450 are disposed or at leastpartially disposed within a hot gas path 18 of the turbine 12. Thevarious stages of the turbine 10 at least partially define the hot gaspath 18 through which combustion gases, as indicated by arrows 20, flowduring operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine nozzle 50 asmay be incorporated in any stage of the turbine 12. FIG. 3 provides across-sectional top view of an airfoil 52 of the turbine nozzle 50 shownin FIG. 2. In one embodiment the turbine nozzle 50 as provided in TableI below is representative of turbine nozzle 400 of the plurality ofturbine nozzles 400 of the fourth stage as shown in FIG. 1. As shown inFIGS. 2 and 3 collectively, the turbine nozzle 50 airfoil 52 includes apressure-side wall 54 and an opposing suction-side wall 56. Thepressure-side wall 54 and the suction-side wall 56 meet or intersect ata leading edge 58 and at a trailing edge 60 of the airfoil 52. A chordline 62 extends between the leading edge 58 and the trailing edge 60such that pressure and suction-side walls 54, 56 can be said to extendin chord or chordwise between the leading edge 58 and the trailing edge60.

As shown in FIG. 2, the airfoil 52 includes a root or first end 64 whichintersects with and extends radially outwardly from an inner band 66 ofthe turbine nozzle 50. The airfoil 52 terminates radially at a secondend or tip 68 of the airfoil 52. The second end 68 intersects with andextends radially inwardly from an outer band 70 of the turbine nozzle50. The pressure and suction-side walls 54, 56 can be said to extend inheight and/or span or in a span-wise direction 72 between the root 64and/or the inner band 66 and the second end 68 or the outer band 70. Inother words, each turbine nozzle 50 includes an airfoil 52 havingopposing pressure and suction-side walls 54, 56 that extend in chord orchordwise 62 between opposing leading and trailing edges 58, 60 and thatextend in span or span-wise 72 between the root 64 and the second end 68of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 74formed between the inner band 66 and the airfoil 52 proximate to theroot 64. The fillet 74 can include a weld or braze fillet, which can beformed via conventional MIG welding, TIG welding, brazing, etc., and caninclude a profile that can reduce fluid dynamic losses as a result ofthe presence of fillet 74. In particular embodiments, the inner band 66,airfoil 52 and the fillet 74 can be formed as a single component, suchas by casting and/or machining and/or 3D printing and/or any othersuitable technique now known or later developed and/or discovered.

The airfoil 52 of the turbine nozzle 50 has a profile at anycross-section taken between the inner band 66 or the root 64 and thesecond end 68. The X, Y, and Z values are given in Table I as percentagevalues of the airfoil length or height/span. As one example only, theheight or radial span of the airfoil 52 of turbine nozzle 50 may be fromabout 5 inches to about 50 inches (about 12 centimeters to about 127centimeters). However, it is to be understood that heights below orabove this range may also be employed as desired in the specificapplication.

The gas turbine hot gas path 18 requires airfoils 52 that meet systemrequirements of aerodynamic and mechanical blade loading and efficiency.To define the airfoil shape of each turbine nozzle airfoil 52, there isa unique set or loci of points in space that meet the stage requirementsand can be manufactured. These unique loci of points meet therequirements for stage efficiency and are arrived at by iterationbetween aerodynamic and mechanical loadings enabling the turbine to runin an efficient, safe and smooth manner. These points are unique andspecific to the system.

The loci that defines the turbine nozzle airfoil profile includes a setof about 2,200 points with X, Y and Z dimensions relative to a referenceorigin coordinate system. The Cartesian coordinate system of X, Y and Zvalues given in Table I below defines the profile of the turbine nozzleairfoil at various locations along its length. Table I lists data for anon-coated airfoil. The envelope/tolerance for the coordinates is about+/−5% in a direction normal to any airfoil surface location and/or about+/−5% of the chord 62 in a direction nominal to any airfoil surfacelocation. The point data origin 76 is defined at or proximate to theleading edge 58 of the airfoil 52 and at or proximate to the root 64.

The coordinate values for the X, Y and Z coordinates are set forth innon-dimensionalized units by the values provided in Table I althoughother units of dimensions may be used when the values are appropriatelyconverted. The X, Y and Z values set forth in Table I are also expressedin non-dimensional form (X, Y, and Z) from 0% to 100% of the height orspan of the airfoil 52. As one example only, the Cartesian coordinatevalues of X, Y and Z may be convertible to dimensional distances bymultiplying the X, Y and Z values by a height of the airfoil at theleading edge 58 and multiplying by a constant number (e.g., 100). As oneexample only, the Cartesian coordinate values of X, Y and Z may beconvertible to dimensional distances by multiplying the X, Y and Zvalues by a height of the airfoil at the trailing edge 60 andmultiplying by a constant number (e.g., 100).

To convert the Z value to a Z coordinate value, e.g., in inches, thenon-dimensional Z value given in Table I is multiplied by the Z lengthof the airfoil in inches. As described above, the Cartesian coordinatesystem has orthogonally-related X, Y and Z axes and the X axis liesgenerally parallel to the turbine rotor centerline, i.e., the rotaryaxis and a positive X coordinate value is axial toward an exhaust end ofthe turbine 14. The positive Y coordinate value extends tangentially inthe direction of rotation of the rotor shaft 14 and the positive Zcoordinate value is radially outwardly toward the second end 68 of theairfoil 52. All the values in Table I are given at room temperature andare non-filleted.

By defining X and Y coordinate values at selected locations in a Zdirection normal to the X, Y plane, the profile section or airfoil shapeof the airfoil 52 of the turbine nozzle 50, at each Z distance along thelength of the airfoil 52 can be ascertained. By connecting the X and Yvalues with smooth continuing arcs, each profile section at eachdistance Z is fixed. The airfoil profiles of the various surfacelocations between the distances Z are determined by smoothly connectingthe adjacent profile sections to one another to form the airfoilprofile.

The Table I values are generated and shown to four decimal places fordetermining the profile of the airfoil. As the turbine nozzle surfaceheats up during operation of the turbine 14, mechanical stresses andelevated temperatures will cause a change in the X, Y and Z values.Accordingly, the values for the profile given in Table I representambient, non-operating or non-hot conditions (e.g., room temperature)and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings whichmust be accounted for in the actual profile of the airfoil 52. Eachsection is joined smoothly with the other sections to form the completeairfoil shape. It will therefore be appreciated that +/− typicalmanufacturing tolerances, i.e., +/− values, including any coatingthicknesses, are additive to the X and Y values given in Table I below.Accordingly, a distance of +/−5% in a direction normal to any surfacelocation along the airfoil profile defines an airfoil profile envelopefor this particular turbine nozzle airfoil design and turbine, i.e., arange of variation between measured points on the actual airfoil surfaceat nominal cold or room temperature and the ideal position of thosepoints as given in the Table below at the same temperature. The data isscalable and the geometry pertains to all aerodynamic scales, at aboveand/or below 3000 RPM. The design of the airfoil 52 of the turbinenozzle 50 is robust to this range of variation without impairment ofmechanical and aerodynamic functions.

TABLE I SUCTION-SIDE PRESSURE-SIDE X (%) Y (%) Z (%) N X (%) Y (%) Z (%)0.0000 0.0000 0.0000 1 0.0000 0.0000 0.0000 −0.1468 −0.3998 0.0000 20.1871 0.2777 0.0000 −0.2206 −0.8187 0.0000 3 0.4405 0.4983 0.0000−0.2127 −1.2445 0.0000 4 0.7294 0.6699 0.0000 −0.1221 −1.6606 0.0000 51.0370 0.8056 0.0000 0.0383 −2.0548 0.0000 6 1.3554 0.9141 0.0000 0.2538−2.4223 0.0000 7 1.6802 1.0023 0.0000 0.5107 −2.7626 0.0000 8 2.00851.0745 0.0000 0.7976 −3.0775 0.0000 9 2.3397 1.1339 0.0000 1.1080−3.3695 0.0000 10 2.6725 1.1834 0.0000 1.4360 −3.6420 0.0000 11 3.00641.2237 0.0000 1.7763 −3.8986 0.0000 12 3.3408 1.2568 0.0000 2.1274−4.1404 0.0000 13 3.6764 1.2840 0.0000 2.4873 −4.3686 0.0000 14 4.01191.3063 0.0000 2.8560 −4.5833 0.0000 15 4.3479 1.3255 0.0000 3.2327−4.7828 0.0000 16 4.6838 1.3430 0.0000 3.6169 −4.9667 0.0000 17 5.01981.3594 0.0000 4.0091 −5.1347 0.0000 18 5.3557 1.3765 0.0000 4.4077−5.2855 0.0000 19 5.6917 1.3945 0.0000 4.8123 −5.4196 0.0000 20 6.02721.4148 0.0000 5.2225 −5.5353 0.0000 21 6.3628 1.4384 0.0000 5.6374−5.6330 0.0000 22 6.6979 1.4655 0.0000 6.0564 −5.7120 0.0000 23 7.03311.4970 0.0000 6.4781 −5.7727 0.0000 24 7.3675 1.5333 0.0000 6.9026−5.8142 0.0000 25 7.7010 1.5752 0.0000 7.3284 −5.8365 0.0000 26 8.03421.6227 0.0000 7.7545 −5.8405 0.0000 27 8.3662 1.6762 0.0000 8.1806−5.8253 0.0000 28 8.6973 1.7356 0.0000 8.6055 −5.7918 0.0000 29 9.02731.8019 0.0000 9.0285 −5.7400 0.0000 30 9.3557 1.8741 0.0000 9.4490−5.6701 0.0000 31 9.6828 1.9531 0.0000 9.8664 −5.5836 0.0000 32 10.00802.0385 0.0000 10.2797 −5.4798 0.0000 33 10.3316 2.1298 0.0000 10.6891−5.3593 0.0000 34 10.6536 2.2276 0.0000 11.0929 −5.2237 0.0000 3510.9736 2.3317 0.0000 11.4915 −5.0728 0.0000 36 11.2916 2.4415 0.000011.8845 −4.9073 0.0000 37 11.6076 2.5568 0.0000 12.2711 −4.7281 0.000038 11.9212 2.6777 0.0000 12.6518 −4.5354 0.0000 39 12.2332 2.8041 0.000013.0252 −4.3303 0.0000 40 12.5428 2.9358 0.0000 13.3919 −4.1129 0.000041 12.8501 3.0727 0.0000 13.7518 −3.8842 0.0000 42 13.1549 3.2143 0.000014.1041 −3.6444 0.0000 43 13.4577 3.3607 0.0000 14.4496 −3.3947 0.000044 13.7582 3.5124 0.0000 14.7876 −3.1345 0.0000 45 14.0558 3.6688 0.000015.1180 −2.8656 0.0000 46 14.3515 3.8296 0.0000 15.4412 −2.5875 0.000047 14.6444 3.9951 0.0000 15.7572 −2.3010 0.0000 48 14.9348 4.1647 0.000016.0656 −2.0066 0.0000 49 15.2225 4.3391 0.0000 16.3664 −1.7049 0.000050 15.5078 4.5174 0.0000 16.6601 −1.3957 0.0000 51 15.7903 4.7002 0.000016.9466 −1.0801 0.0000 52 16.0700 4.8865 0.0000 17.2255 −0.7577 0.000053 16.3473 5.0772 0.0000 17.4972 −0.4293 0.0000 54 16.6218 5.2715 0.000017.7621 −0.0950 0.0000 55 16.8939 5.4694 0.0000 18.0195 0.2446 0.0000 5617.1632 5.6709 0.0000 18.2696 0.5897 0.0000 57 17.4297 5.8760 0.000018.5130 0.9396 0.0000 58 17.6939 6.0847 0.0000 18.7496 1.2943 0.0000 5917.9552 6.2962 0.0000 18.9802 1.6530 0.0000 60 18.2138 6.5112 0.000019.2053 2.0149 0.0000 61 18.4699 6.7295 0.0000 19.4259 2.3800 0.0000 6218.7237 6.9501 0.0000 19.6426 2.7471 0.0000 63 18.9747 7.1740 0.000019.8560 3.1158 0.0000 64 19.2232 7.4006 0.0000 20.0675 3.4864 0.0000 6519.4694 7.6300 0.0000 20.2766 3.8579 0.0000 66 19.7128 7.8622 0.000020.4845 4.2302 0.0000 67 19.9542 8.0964 0.0000 20.6907 4.6028 0.0000 6820.1928 8.3334 0.0000 20.8966 4.9763 0.0000 69 20.4294 8.5728 0.000021.1013 5.3501 0.0000 70 20.6632 8.8142 0.0000 21.3056 5.7244 0.0000 7120.8950 9.0580 0.0000 21.5095 6.0987 0.0000 72 21.1248 9.3042 0.000021.7130 6.4733 0.0000 73 21.3519 9.5520 0.0000 21.9161 6.8484 0.0000 7421.5769 9.8021 0.0000 22.1187 7.2234 0.0000 75 21.8000 10.0539 0.000022.3214 7.5985 0.0000 76 22.0210 10.3077 0.0000 22.5241 7.9735 0.0000 7722.2396 10.5630 0.0000 22.7264 8.3486 0.0000 78 22.4563 10.8204 0.000022.9287 8.7241 0.0000 79 22.6710 11.0793 0.0000 23.1310 9.0991 0.0000 8022.8836 11.3403 0.0000 23.3329 9.4746 0.0000 81 23.0943 11.6024 0.000023.5348 9.8500 0.0000 82 23.3030 11.8661 0.0000 23.7371 10.2255 0.000083 23.5100 12.1315 0.0000 23.9390 10.6009 0.0000 84 23.7151 12.39800.0000 24.1409 10.9764 0.0000 85 23.9186 12.6657 0.0000 24.3428 11.35180.0000 86 24.1201 12.9351 0.0000 24.5450 11.7273 0.0000 87 24.320013.2056 0.0000 24.7469 12.1027 0.0000 88 24.5179 13.4777 0.0000 24.949212.4778 0.0000 89 24.7142 13.7506 0.0000 25.1511 12.8533 0.0000 9024.9093 14.0251 0.0000 25.3534 13.2287 0.0000 91 25.1020 14.3004 0.000025.5557 13.6038 0.0000 92 25.2932 14.5773 0.0000 25.7580 13.9792 0.000093 25.4827 14.8554 0.0000 25.9603 14.3543 0.0000 94 25.6706 15.13430.0000 26.1626 14.7297 0.0000 95 25.8585 15.4132 0.0000 26.3653 15.10480.0000 96 26.0461 15.6925 0.0000 26.5676 15.4799 0.0000 97 26.231615.9730 0.0000 26.7706 15.8549 0.0000 98 26.4119 16.2571 0.0000 26.899916.5990 0.0000 99 26.5991 16.5364 0.0000 26.9745 16.2292 0.0000 10026.8999 16.5990 0.0000 −0.6667 −1.6642 10.0000 1 −0.6667 −1.6642 10.0000−0.7816 −2.0919 10.0000 2 −0.4964 −1.3494 10.0000 −0.8120 −2.533210.0000 3 −0.2534 −1.0857 10.0000 −0.7493 −2.9713 10.0000 4 0.0347−0.8718 10.0000 −0.6009 −3.3883 10.0000 5 0.3483 −0.6970 10.0000 −0.3826−3.7737 10.0000 6 0.6779 −0.5542 10.0000 −0.1129 −4.1252 10.0000 71.0162 −0.4345 10.0000 0.1935 −4.4452 10.0000 8 1.3610 −0.3332 10.00000.5267 −4.7377 10.0000 9 1.7097 −0.2474 10.0000 0.8798 −5.0062 10.000010 2.0616 −0.1748 10.0000 1.2469 −5.2544 10.0000 11 2.4155 −0.112510.0000 1.6251 −5.4858 10.0000 12 2.7702 −0.0575 10.0000 2.0117 −5.702510.0000 13 3.1261 −0.0068 10.0000 2.4063 −5.9047 10.0000 14 3.48200.0415 10.0000 2.8077 −6.0923 10.0000 15 3.8379 0.0890 10.0000 3.2167−6.2638 10.0000 16 4.1942 0.1361 10.0000 3.6317 −6.4194 10.0000 174.5502 0.1839 10.0000 4.0530 −6.5579 10.0000 18 4.9061 0.2326 10.00004.4791 −6.6796 10.0000 19 5.2620 0.2821 10.0000 4.9100 −6.7837 10.000020 5.6175 0.3328 10.0000 5.3450 −6.8699 10.0000 21 5.9730 0.3846 10.00005.7830 −6.9381 10.0000 22 6.3285 0.4381 10.0000 6.2235 −6.9884 10.000023 6.6832 0.4944 10.0000 6.6656 −7.0199 10.0000 24 7.0375 0.5530 10.00007.1085 −7.0335 10.0000 25 7.3914 0.6149 10.0000 7.5518 −7.0287 10.000026 7.7445 0.6799 10.0000 7.9947 −7.0060 10.0000 27 8.0972 0.7481 10.00008.4360 −6.9653 10.0000 28 8.4495 0.8199 10.0000 8.8757 −6.9070 10.000029 8.8007 0.8953 10.0000 9.3126 −6.8320 10.0000 30 9.1510 0.9747 10.00009.7463 −6.7398 10.0000 31 9.5001 1.0585 10.0000 10.1760 −6.6321 10.000032 9.8484 1.1463 10.0000 10.6017 −6.5080 10.0000 33 10.1955 1.238910.0000 11.0227 −6.3688 10.0000 34 10.5415 1.3362 10.0000 11.4384−6.2148 10.0000 35 10.8858 1.4380 10.0000 11.8486 −6.0464 10.0000 3611.2289 1.5449 10.0000 12.2528 −5.8648 10.0000 37 11.5705 1.6566 10.000012.6514 −5.6701 10.0000 38 11.9100 1.7735 10.0000 13.0432 −5.463110.0000 39 12.2476 1.8960 10.0000 13.4286 −5.2440 10.0000 40 12.58352.0233 10.0000 13.8069 −5.0134 10.0000 41 12.9175 2.1562 10.0000 14.1787−4.7716 10.0000 42 13.2491 2.2946 10.0000 14.5438 −4.5202 10.0000 4313.5782 2.4383 10.0000 14.9017 −4.2585 10.0000 44 13.9050 2.5871 10.000015.2528 −3.9880 10.0000 45 14.2294 2.7415 10.0000 15.5968 −3.707910.0000 46 14.5510 2.9015 10.0000 15.9331 −3.4190 10.0000 47 14.86983.0667 10.0000 16.2623 −3.1221 10.0000 48 15.1862 3.2375 10.0000 16.5847−2.8177 10.0000 49 15.4994 3.4134 10.0000 16.8999 −2.5061 10.0000 5015.8094 3.5942 10.0000 17.2083 −2.1877 10.0000 51 16.1170 3.7805 10.000017.5099 −1.8629 10.0000 52 16.4211 3.9712 10.0000 17.8048 −1.531710.0000 53 16.7223 4.1671 10.0000 18.0925 −1.1946 10.0000 54 17.02044.3678 10.0000 18.3730 −0.8515 10.0000 55 17.3152 4.5729 10.0000 18.6467−0.5023 10.0000 56 17.6069 4.7824 10.0000 18.9132 −0.1480 10.0000 5717.8958 4.9962 10.0000 19.1730 0.2111 10.0000 58 18.1811 5.2141 10.000019.4263 0.5750 10.0000 59 18.4639 5.4359 10.0000 19.6741 0.9424 10.000060 18.7432 5.6618 10.0000 19.9163 1.3139 10.0000 61 19.0197 5.890810.0000 20.1541 1.6882 10.0000 62 19.2935 6.1238 10.0000 20.3875 2.064810.0000 63 19.5640 6.3600 10.0000 20.6177 2.4439 10.0000 64 19.83176.5998 10.0000 20.8444 2.8249 10.0000 65 20.0962 6.8424 10.0000 21.06863.2075 10.0000 66 20.3584 7.0886 10.0000 21.2900 3.5914 10.0000 6720.6173 7.3371 10.0000 21.5099 3.9764 10.0000 68 20.8735 7.5889 10.000021.7285 4.3622 10.0000 69 21.1272 7.8435 10.0000 21.9452 4.7489 10.000070 21.3782 8.1004 10.0000 22.1614 5.1359 10.0000 71 21.6264 8.360210.0000 22.3765 5.5233 10.0000 72 21.8718 8.6223 10.0000 22.5912 5.911510.0000 73 22.1152 8.8868 10.0000 22.8050 6.2997 10.0000 74 22.35589.1534 10.0000 23.0189 6.6880 10.0000 75 22.5936 9.4227 10.0000 23.23237.0766 10.0000 76 22.8294 9.6936 10.0000 23.4450 7.4656 10.0000 7723.0628 9.9669 10.0000 23.6581 7.8546 10.0000 78 23.2938 10.2418 10.000023.8703 8.2437 10.0000 79 23.5224 10.5187 10.0000 24.0826 8.6327 10.000080 23.7490 10.7976 10.0000 24.2949 9.0221 10.0000 81 23.9733 11.078110.0000 24.5063 9.4115 10.0000 82 24.1955 11.3606 10.0000 24.7182 9.801310.0000 83 24.4154 11.6443 10.0000 24.9293 10.1912 10.0000 84 24.633611.9300 10.0000 25.1403 10.5810 10.0000 85 24.8499 12.2169 10.000025.3514 10.9708 10.0000 86 25.0645 12.5049 10.0000 25.5625 11.360610.0000 87 25.2772 12.7942 10.0000 25.7732 11.7508 10.0000 88 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15.74642.5129 20.0001 17.4301 −3.3288 20.0001 50 16.0827 2.6952 20.0001 17.7545−3.0008 20.0001 51 16.4155 2.8831 20.0001 18.0717 −2.6669 20.0001 5216.7455 3.0767 20.0001 18.3825 −2.3265 20.0001 53 17.0722 3.2754 20.000118.6866 −1.9798 20.0001 54 17.3954 3.4796 20.0001 18.9838 −1.627920.0001 55 17.7154 3.6891 20.0001 19.2747 −1.2700 20.0001 56 18.03223.9038 20.0001 19.5588 −0.9073 20.0001 57 18.3454 4.1232 20.0001 19.8365−0.5394 20.0001 58 18.6555 4.3471 20.0001 20.1078 −0.1668 20.0001 5918.9619 4.5761 20.0001 20.3731 0.2099 20.0001 60 19.2647 4.8095 20.000120.6329 0.5905 20.0001 61 19.5644 5.0469 20.0001 20.8874 0.9747 20.000162 19.8604 5.2891 20.0001 21.1376 1.3622 20.0001 63 20.1533 5.535320.0001 21.3834 1.7520 20.0001 64 20.4426 5.7850 20.0001 21.6260 2.143820.0001 65 20.7286 6.0392 20.0001 21.8654 2.5380 20.0001 66 21.01116.2966 20.0001 22.1020 2.9334 20.0001 67 21.2904 6.5579 20.0001 22.33623.3304 20.0001 68 21.5665 6.8228 20.0001 22.5684 3.7286 20.0001 6921.8391 7.0910 20.0001 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35.7943 11.8354 90.0000 94 35.101312.5987 90.0000 36.0549 12.3681 90.0000 95 35.4193 13.0404 90.000036.3130 12.9019 90.0000 96 35.7353 13.4841 90.0000 36.5696 13.436690.0000 97 36.0493 13.9286 90.0000 36.8253 13.9716 90.0000 98 36.364514.3722 90.0000 37.0779 14.5083 90.0000 99 36.6765 14.8183 90.000037.0979 15.0390 90.0000 100 37.0979 15.0390 90.0000 −5.9171 −16.1550100.0000 1 −5.9171 −16.1550 100.0000 −5.6562 −16.7060 100.0000 2 −6.0324−15.6003 100.0000 −5.2380 −17.1508 100.0000 3 −6.0576 −15.0346 100.0000−4.7261 −17.4856 100.0000 4 −5.9786 −14.4740 100.0000 −4.1663 −17.7330100.0000 5 −5.7922 −13.9397 100.0000 −3.5822 −17.9169 100.0000 6 −5.5105−13.4482 100.0000 −2.9853 −18.0530 100.0000 7 −5.1538 −13.0081 100.0000−2.3812 −18.1535 100.0000 8 −4.7429 −12.6183 100.0000 −1.7727 −18.2253100.0000 9 −4.2928 −12.2735 100.0000 −1.1623 −18.2748 100.0000 10−3.8148 −11.9691 100.0000 −0.5506 −18.3083 100.0000 11 −3.3208 −11.6910100.0000 0.0614 −18.3291 100.0000 12 −2.8181 −11.4288 100.0000 0.6739−18.3371 100.0000 13 −2.3090 −11.1791 100.0000 1.2864 −18.3323 100.000014 −1.7947 −10.9401 100.0000 1.8984 −18.3139 100.0000 15 −1.2764−10.7111 100.0000 2.5105 −18.2828 100.0000 16 −0.7537 −10.4908 100.00003.1213 −18.2381 100.0000 17 −0.2278 −10.2785 100.0000 3.7310 −18.1807100.0000 18 0.3004 −10.0731 100.0000 4.3395 −18.1096 100.0000 19 0.8311−9.8736 100.0000 4.9460 −18.0254 100.0000 20 1.3634 −9.6788 100.00005.5508 −17.9285 100.0000 21 1.8976 −9.4881 100.0000 6.1533 −17.8180100.0000 22 2.4327 −9.3006 100.0000 6.7534 −17.6947 100.0000 23 2.9685−9.1159 100.0000 7.3503 −17.5582 100.0000 24 3.5052 −8.9323 100.00007.9448 −17.4094 100.0000 25 4.0422 −8.7504 100.0000 8.5353 −17.2482100.0000 26 4.5793 −8.5688 100.0000 9.1230 −17.0742 100.0000 27 5.1163−8.3869 100.0000 9.7064 −16.8883 100.0000 28 5.6530 −8.2046 100.000010.2861 −16.6904 100.0000 29 6.1896 −8.0214 100.0000 10.8615 −16.4805100.0000 30 6.7255 −7.8367 100.0000 11.4324 −16.2591 100.0000 31 7.2609−7.6500 100.0000 11.9990 −16.0261 100.0000 32 7.7956 −7.4612 100.000012.5608 −15.7823 100.0000 33 8.3294 −7.2705 100.0000 13.1178 −15.5273100.0000 34 8.8625 −7.0774 100.0000 13.6700 −15.2620 100.0000 35 9.3948−6.8815 100.0000 14.2170 −14.9859 100.0000 36 9.9258 −6.6828 100.000014.7585 −14.7002 100.0000 37 10.4557 −6.4813 100.0000 15.2947 −14.4042100.0000 38 10.9844 −6.2770 100.0000 15.8258 −14.0989 100.0000 3911.5118 −6.0691 100.0000 16.3513 −13.7841 100.0000 40 12.0381 −5.8581100.0000 16.8712 −13.4605 100.0000 41 12.5632 −5.6434 100.0000 17.3855−13.1278 100.0000 42 13.0863 −5.4252 100.0000 17.8942 −12.7866 100.000043 13.6082 −5.2033 100.0000 18.3973 −12.4371 100.0000 44 14.1281 −4.9775100.0000 18.8945 −12.0792 100.0000 45 14.6463 −4.7477 100.0000 19.3860−11.7141 100.0000 46 15.1627 −4.5134 100.0000 19.8720 −11.3411 100.000047 15.6774 −4.2752 100.0000 20.3524 −10.9608 100.0000 48 16.1897 −4.0331100.0000 20.8268 −10.5734 100.0000 49 16.7004 −3.7861 100.0000 21.2956−10.1792 100.0000 50 17.2083 −3.5347 100.0000 21.7585 −9.7782 100.000051 17.7142 −3.2790 100.0000 22.2157 −9.3704 100.0000 52 18.2182 −3.0184100.0000 22.6674 −8.9567 100.0000 53 18.7189 −2.7531 100.0000 23.1134−8.5369 100.0000 54 19.2176 −2.4830 100.0000 23.5535 −8.1112 100.0000 5519.7136 −2.2080 100.0000 23.9884 −7.6795 100.0000 56 20.2068 −1.9283100.0000 24.4174 −7.2426 100.0000 57 20.6967 −1.6435 100.0000 24.8411−6.8001 100.0000 58 21.1843 −1.3538 100.0000 25.2592 −6.3524 100.0000 5921.6687 −1.0589 100.0000 25.6722 −5.9000 100.0000 60 22.1499 −0.7593100.0000 26.0796 −5.4427 100.0000 61 22.6275 −0.4541 100.0000 26.4814−4.9803 100.0000 62 23.1023 −0.1440 100.0000 26.8780 −4.5138 100.0000 6323.5735 0.1712 100.0000 27.2694 −4.0426 100.0000 64 24.0411 0.4920100.0000 27.6556 −3.5670 100.0000 65 24.5051 0.8175 100.0000 28.0367−3.0874 100.0000 66 24.9656 1.1483 100.0000 28.4125 −2.6038 100.0000 6725.4220 1.4847 100.0000 28.7832 −2.1163 100.0000 68 25.8749 1.8258100.0000 29.1491 −1.6251 100.0000 69 26.3238 2.1721 100.0000 29.5102−1.1300 100.0000 70 26.7687 2.5237 100.0000 29.8661 −0.6316 100.0000 7127.2091 2.8804 100.0000 30.2176 −0.1301 100.0000 72 27.6460 3.2422100.0000 30.5639 0.3751 100.0000 73 28.0782 3.6093 100.0000 30.90580.8834 100.0000 74 28.5059 3.9812 100.0000 31.2434 1.3945 100.0000 7528.9296 4.3578 100.0000 31.5762 1.9088 100.0000 76 29.3486 4.7397100.0000 31.9045 2.4259 100.0000 77 29.7631 5.1267 100.0000 32.22892.9454 100.0000 78 30.1733 5.5181 100.0000 32.5489 3.4677 100.0000 7930.5791 5.9143 100.0000 32.8649 3.9924 100.0000 80 30.9801 6.3153100.0000 33.1765 4.5198 100.0000 81 31.3763 6.7207 100.0000 33.48465.0493 100.0000 82 31.7681 7.1305 100.0000 33.7890 5.5808 100.0000 8332.1551 7.5446 100.0000 34.0894 6.1146 100.0000 84 32.5377 7.9628100.0000 34.3859 6.6505 100.0000 85 32.9160 8.3857 100.0000 34.67877.1883 100.0000 86 33.2894 8.8122 100.0000 34.9684 7.7282 100.0000 8733.6581 9.2427 100.0000 35.2549 8.2696 100.0000 88 34.0228 9.6769100.0000 35.5378 8.8130 100.0000 89 34.3835 10.1142 100.0000 35.81799.3577 100.0000 90 34.7402 10.5550 100.0000 36.0952 9.9039 100.0000 9135.0933 10.9987 100.0000 36.3693 10.4517 100.0000 92 35.4420 11.4456100.0000 36.6406 11.0007 100.0000 93 35.7872 11.8953 100.0000 36.908711.5513 100.0000 94 36.1287 12.3481 100.0000 37.1741 12.1035 100.0000 9536.4666 12.8034 100.0000 37.4366 12.6570 100.0000 96 36.8014 13.2610100.0000 37.6964 13.2116 100.0000 97 37.1330 13.7207 100.0000 37.954513.7674 100.0000 98 37.4625 14.1823 100.0000 38.2087 14.3244 100.0000 9937.7889 14.6456 100.0000 38.2262 14.8750 100.0000 100 38.2262 14.8750100.0000

It will also be appreciated that the airfoil 52 disclosed in the aboveTable I may be scaled up or down geometrically for use in other similarturbine designs. Consequently, the coordinate values set forth in TableI may be scaled upwardly or downwardly such that the airfoil profileshape remains unchanged. A scaled version of the coordinates in Table Iwould be represented by X, Y and Z coordinate values of Table I, withthe X, Y and Z non-dimensional coordinate values converted to inches,multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is therange of the variation between measured points on an airfoil surface andthe ideal position listed in Table I. The actual profile on amanufactured turbine nozzle will be different than those in Table I andthe design is robust to this variation meaning that mechanical andaerodynamic function are not impaired. As noted above, a + or −5%profile tolerance is used herein. The X, Y and Z values are allnon-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machineconditions and specifications. It provides a unique profile toachieve 1) interaction between other stages in the turbine 10; 2)aerodynamic efficiency; and 3) normalized aerodynamic and mechanicalnozzle or airfoil loadings. The disclosed loci of points defined inTable I allow the gas turbine 12 or any other suitable turbine to run inan efficient, safe and smooth manner. As also noted, any scale of thedisclosed airfoil 52 may be adopted as long as 1) interaction betweenother stages in the pressure turbine 10; 2) aerodynamic efficiency; and3) normalized aerodynamic and mechanical nozzle or airfoil loadings aremaintained in the scaled turbine.

The airfoil 52 described herein thus improves overall gas turbine 12efficiency. Specifically, the airfoil 52 provides a desired turbineefficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52also meets all aeromechanics and stress requirements. The turbine nozzle50 described herein has very specific aerodynamic design requirementssuch as an upstream bucket radial back pressure (i.e., work splits) andradial velocity triangles for the downstream turbine rotors 150, 250,350 and 450. Significant cross-functional design effort was require tomeet these design goals. The airfoil 52 of the turbine nozzle 50 thus isof a specific shape to meet aerodynamic, mechanical, and heat transferrequirements in an efficient and cost effective manner.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

What is claimed is:
 1. A turbine nozzle comprising an airfoil shape, theairfoil shape having a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in Table I whereinthe Cartesian coordinate values of X, Y and Z are non-dimensional valuesfrom 0% to 100% convertible to dimensional distances in inches bymultiplying the Cartesian coordinate values of X, Y and Z by a height ofthe airfoil in inches, and wherein X and Y, when connected by smoothcontinuing arcs, define airfoil profile sections at each distance Z, theairfoil profile sections at Z distances being joined smoothly with oneanother to form a complete airfoil shape.
 2. The turbine nozzle of claim1, wherein the turbine nozzle forms part of a stage of a turbine.
 3. Theturbine nozzle of claim 1, wherein the turbine nozzle is a fourth stageturbine nozzle.
 4. The turbine nozzle of claim 1, wherein the airfoilshape lies in an envelope within at least one of +/−5% and/or +/−5% of achord length in a direction normal to any airfoil surface location. 5.The turbine nozzle of claim 1, wherein a height of the turbine nozzle isabout 5 inches to about 50 inches (about 12 centimeters to about 127centimeters) in length.
 6. The turbine nozzle of claim 1, wherein the X,Y and Z distances are scalable as a function of the same constant ornumber to provide a scaled-up or scaled-down airfoil.
 7. A turbinenozzle comprising a an airfoil having a suction-side uncoated nominalairfoil profile substantially in accordance with suction-side Cartesiancoordinate values of X, Y and Z set forth in Table I wherein theCartesian coordinate values of X, Y and Z are non-dimensional valuesfrom 0% to 100% convertible to dimensional distances in inches bymultiplying the Cartesian coordinate values of X, Y and Z by a height ofthe airfoil in inches, and wherein X and Y, when connected by smoothcontinuing arcs, define airfoil profile sections at each Z distance, theairfoil profile sections at the Z distances being joined smoothly withone another to form a complete suction-side airfoil shape, the X, Y andZ distances being scalable as a function of the same constant or numberto provide a scaled-up or scaled-down airfoil.
 8. The turbine nozzle ofclaim 7, wherein the turbine nozzle forms part of a stage of a turbine.9. The turbine nozzle of claim 7, wherein the turbine nozzle is a fourthstage turbine nozzle.
 10. The turbine nozzle of claim 7, wherein theairfoil shape lies in an envelope within at least one of +/−5% and/or+/−5% of a chord length in a direction normal to any airfoil surfacelocation.
 11. The turbine nozzle of claim 7, wherein a height of theturbine nozzle is about 5 inches to about 50 inches (about 12centimeters to about 130 centimeters) in length.
 12. A turbinecomprising a plurality of turbine nozzles, each of the turbine nozzlescomprising an airfoil having an airfoil shape, the airfoil having anominal profile substantially in accordance with Cartesian coordinatevalues of X, Y and Z set forth in Table I wherein the Cartesiancoordinate values of X, Y and Z are non-dimensional values from 0% to100% convertible to dimensional distances in inches by multiplying theCartesian coordinate values of X, Y and Z by a height of the airfoil ininches, and wherein X and Y, when connected by smooth continuing arcs,define airfoil profile sections at each Z distance, the airfoil profilesections at Z distances being joined smoothly with one another to form acomplete airfoil shape.
 13. The turbine of claim 12, wherein theplurality of turbine nozzles forms part of a stage of a turbine.
 14. Theturbine of claim 12, wherein the plurality of turbine nozzles comprisesa plurality of fourth stage turbine nozzles.
 15. The turbine of claim12, wherein the airfoil shape lies in an envelope within at least one of+/−5% and/or +/−5% of a chord length in a direction normal to anyairfoil surface location.
 16. The turbine of claim 12, wherein a heightthe turbine nozzle is about 5 inches to about 50 inches (about 12centimeters to about 127 centimeters) in length.
 17. The turbine ofclaim 12, wherein the X, Y and Z distances are scalable as a function ofthe same constant or number to provide a scaled-up or scaled-downairfoil.
 18. The turbine of claim 12, wherein X represents a distanceparallel to a turbine axis of rotation.